The doctoral dissertations of the former Helsinki University of Technology (TKK) and Aalto University Schools of Technology (CHEM, ELEC, ENG, SCI) published in electronic format are available in the electronic publications archive of Aalto University - Aaltodoc.
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Regularization Methods for Diffuse Optical Tomography

Petri Hiltunen

Doctoral dissertation for the degree of Doctor of Science in Technology to be presented with due permission of the School of Science for public examination and debate in Auditorium E at the Aalto University School of Science (Espoo, Finland) on the 8th of November 2011 at 12 noon.

Overview in PDF format (ISBN 978-952-60-4321-0)   [272 KB]
Dissertation is also available in print (ISBN 978-952-60-4320-3)

Abstract

Near-infrared light can be used as a three dimensional imaging tool, called diffuse optical tomography (DOT), in the study of human physiology. Due to differences in the extinction coefficients of oxygenated and deoxygenated haemoglobin at different wavelengths, concentrations of the haemoglobins can be resolved from measurements at a few wavelengths. Therefore, DOT is a fascinating modality for biomedical applications, such as functional brain imaging, breast cancer screening, etc. Moreover light is a safe tool, because it is non-ionizing and at intensity levels used in DOT, it does not cause burns at skin or in organs.

There are a few different models to describe light propagation in tissue-like media. One of the simplest, called the diffusion approximation (DA), was used in this thesis. The optical properties, the absorption and the scattering coefficients, are the parameters which determine the light propagation in the DA model. When optical properties are known and one is interested in estimating the photon flux at the boundary, the problem is called a forward problem. Likewise, when the photon flux at the boundary is measured and the task is to find the optical properties, the problem is called an inverse problem. The inverse problem related to DOT is ill-posed, i.e., the solution might not be unique or the solution does not depend continuously on data.

Due to ill-posedness of the inverse problem, some regularization methods should be used. In this thesis, regularization methods for a stationary and nonstationary inverse problems was considered. By the nonstationary inverse problem, it is meant that the optical properties are not static during the measurement and the whole evolution of the optical properties is reconstructed in contrast to the stationary problem, where the optical properties are assumed to be static during the measurement.

The regularization for the inverse problem could be implemented as the Tikhonov regularization or using statistical inversion theory, also known as the Bayesian framework. In this thesis, two different regularization methods for the static reconstruction problem in DOT were studied. They both allow discontinuities in the optical properties that might occur at boundaries between organs. For the nonstationary reconstruction problem, an efficient regularization model is presented.

This thesis consists of an overview and of the following 4 publications:

  1. P. Hiltunen, D. Calvetti, and E. Somersalo. An adaptive smoothness regularization algorithm for optical tomography. Optics Express, 16(24), 19957-19977, 2008. © 2008 Optical Society of America (OSA). By permission.
  2. J. Heiskala, P. Hiltunen and I. Nissilä. Significance of background optical properties, time-resolved information and optode arrangement in diffuse optical imaging of term neonates. Physics in Medicine and Biology, 54(3), 535-554, 2009. © 2009 Institute of Physics and Engineering in Medicine (IPEM). By permission.
  3. P. Hiltunen, S.J.D. Prince, and S. Arridge. A combined reconstruction–classification method for diffuse optical tomography. Physics in Medicine and Biology, 54(21), 6457-6476, 2009. © 2009 Institute of Physics and Engineering in Medicine (IPEM). By permission.
  4. P. Hiltunen, S. Särkkä, I. Nissilä, A. Lajunen, and J. Lampinen. State space regularization in the nonstationary inverse problem for diffuse optical tomography. Inverse problems, 27(2), 025009 (15 pages), 2011. © 2011 Institute of Physics Publishing (IOPP). By permission.

Keywords: diffuse optical tomography, inverse problem, regularization

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© 2011 Aalto University

Last update 2012-02-15